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function b = gee_its_simple_backsolve (U, b)
%GEE_ITS_SIMPLE_BACKSOLVE x=U\b where U is upper triangular
% Perform back substitution to solve x=U\b. U must be square. The lower
% triangular part of U is ignored (this allows L and U to be packed into a
% single matrix).
%
% Example:
%
% x = gee_its_simple_backsolve (U,b) ;
%
% % which is the same as
% x = triu (U) \ b ;
%
% See also: mldivide, gee_its_simple, gee_its_short, gee_its_simple_forwardsolve
% GEE, Copyright (c) 2006-2007, Timothy A Davis. All Rights Reserved.
% SPDX-License-Identifier: BSD-3-clause
%-------------------------------------------------------------------------------
% check inputs
%-------------------------------------------------------------------------------
if (nargin ~= 2 | nargout > 1) %#ok
error ('Usage: x = ge_its_simple_backsolve (U,b)') ;
end
% ensure U is square, and that U and b have the same number of rows
gee_its_simple_check (U, 'U', b) ;
%-------------------------------------------------------------------------------
% backsolve solve, overwriting b with the solution U\b
%-------------------------------------------------------------------------------
n = size (U,1) ;
for k = n:-1:1
b (k,:) = b (k,:) / U (k,k) ;
b (1:k-1,:) = b (1:k-1,:) - U (1:k-1,k) * b (k,:) ;
end
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